When God confused the languages at Babel, He effectively ended the world's first great building project. Some have doubtless deduced from this that dialects are a God-ordained partition between people and cultures, but that would directly contradict Christ's later command to "go into all the world and preach the Gospel."
This is of course the most obvious reason for learning a foreign language: to share the truth of Christ's redemption with every tribe and nation. Whether you intend to actually go overseas, translate Scripture, or simply to witness to a local community, the first step toward communication is to learn the language of the group you intend to impact.
Obviously, acquiring skills in the local speech is necessary just to talk to people and be understood, but it's also important for learning about the community. The ideas and attitudes of a culture are embedded in its dominant tongue, and to effectively communicate the Gospel (or any message) with a foreign society one needs to "get" where its members are coming from.
This is as true of past cultures as present ones. While you certainly don't need to be proficient in biblical languages to study the Bible, a knowledge of Hebrew and Koine Greek will deepen your understanding of God's Word and the cultural and religious contexts in which it was written. To properly and accurately translate the Bible, knowing the original languages thoroughly is crucial.
It's easy to think of all these uses for language in Anglo-centric terms. English is the most widely spoken language in the world today, and the universal language for business; we tend to think of translation purely in terms of our own language, communication in terms of our Western understanding.
Such a truncated view is harmful both to our work as Christians and to our personal outlook. English may be dominant now, but it wasn't always so, and won't maintain that position forever. The language of Heaven isn't English, and God never set the English-speaking world apart for special treatment or honor.
Ironically, English isn't even the official language of the United States. It's the de facto (most prevalent) language, but there is no "offical language" in our nation. There are several reasons for this, but in the end such an omission on the part of the Federal government underscores a very American idea: all people are created equal.
Which, in a way, is also a very biblical concept. All mankind is born in sin, unable to communicate directly with God until Christ's redeeming grace and love bring us to reconciliation with Him. This is the message that ought to motivate all our attempts at communication, and the sharing of which should drive us to study foreign languages of every kind.